21ST CENTURY ASTR.:SOLAR..(LL)-PACKAGE
6th Edition
ISBN: 9780393448498
Author: Kay
Publisher: NORTON
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Chapter 13, Problem 40QP
To determine
The uncertainty in the measurement.
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In the parallax method of determining stellar distances, the angle to a star is measured while
the earth is on one side of the sun and then again six months later, as in the diagram below.
Assume the earth-sun distance is 1 Astronomical Unit. The parallax angle of Alpha Centauri
is 0= 2.1 x 10-4 ° . Find the distance from the sun to a Centauri in light years. Assume a
circular orbit for the Earth.
a Centauri
Earth (June)
Earth (December)
Sun
If we view a star now, and then view it again 6 months later, our position will have changed by the diameter of the Earth's orbit around the sun. For nearby stars (within 100 light-years or so), the change in viewing location is sufficient to make the star appear to be in a slightly different location in the sky. Half of the angle from one location to the next is known as the parallax angle (see figure). Parallax can be used to measure the distance to the star. An approximate relationship is given by
d =
3.26
p
,
where d is the distance in light-years, and p is the parallax measured in seconds of arc. Vega is a star that has a parallax angle of 0.13 second. How far is Vega from the sun? Note: Parallax is used not only to measure stellar distances. Our binocular vision actually provides the brain with a parallax angle that it uses to estimate distances to objects we see. (Round your answer to two decimal places.) light-years
Solve the following problem:
Two stars, named A and B, each with a mass equal to the Sun's mass are in orbit around each other. If the distance between the two stars is 1.0 AU. What is the period of their orbit?
Describe each step in solving the problem:
Chapter 13 Solutions
21ST CENTURY ASTR.:SOLAR..(LL)-PACKAGE
Ch. 13.1 - Prob. 13.1CYUCh. 13.2 - Prob. 13.2CYUCh. 13.3 - Prob. 13.3CYUCh. 13.4 - Prob. 13.4CYUCh. 13 - Prob. 1QPCh. 13 - Prob. 2QPCh. 13 - Prob. 3QPCh. 13 - Prob. 4QPCh. 13 - Prob. 5QPCh. 13 - Prob. 6QP
Ch. 13 - Prob. 7QPCh. 13 - Prob. 8QPCh. 13 - Prob. 9QPCh. 13 - Prob. 10QPCh. 13 - Prob. 11QPCh. 13 - Prob. 12QPCh. 13 - Prob. 13QPCh. 13 - Prob. 14QPCh. 13 - Prob. 15QPCh. 13 - Prob. 16QPCh. 13 - Prob. 17QPCh. 13 - Prob. 18QPCh. 13 - Prob. 19QPCh. 13 - Prob. 20QPCh. 13 - Prob. 21QPCh. 13 - Prob. 22QPCh. 13 - Prob. 23QPCh. 13 - Prob. 24QPCh. 13 - Prob. 25QPCh. 13 - Prob. 26QPCh. 13 - Prob. 27QPCh. 13 - Prob. 28QPCh. 13 - Prob. 29QPCh. 13 - Prob. 30QPCh. 13 - Prob. 31QPCh. 13 - Prob. 32QPCh. 13 - Prob. 33QPCh. 13 - Prob. 34QPCh. 13 - Prob. 35QPCh. 13 - Prob. 36QPCh. 13 - Prob. 37QPCh. 13 - Prob. 38QPCh. 13 - Prob. 39QPCh. 13 - Prob. 40QPCh. 13 - Prob. 41QPCh. 13 - Prob. 42QPCh. 13 - Prob. 43QPCh. 13 - Prob. 44QPCh. 13 - Prob. 45QP
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- The star Sirius has an apparent magnitude of -1.46 and appears 95-times brighter compared tothe more distant star Tau Ceti, which has an absolute magnitude of 5.69.(a) Explain the terms apparent magnitude, absolute magnitude and bolometric magnitude.(b) Calculate the apparent magnitude of the star Tau Ceti.(c) Find the distance between the Earth and Tau Ceti.www.arrow_forwardThe nearest star to our solar system is 4.29 light years away. How much is thisdistance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun ?arrow_forwardUse a diagram to explain what is meant by the parallax angle, p, for a star observed twice from Earth, with a 6-month interval between each observation. Hence define the parsec, and calculate its value in astronomical units and metres. The star Betelgeuse is observed to have a parallax angle p = 4.5 × 10−3 arcseconds. State the distance of Betelgeuse in units of parsecs and light years.arrow_forward
- Assume that there are 2 stars - Aqua and Ruby. They are in orbit around a massive star which is named as Star Ai that has a mass 5.98 x 1028 kg. The orbit of Ruby is circle and has a period of 1.430 yrs. The orbit of Aqua is an ellipse. At its periapsis, the distance of Star Aqua is twice as far from Star Ai than Star Ruby is. Solve how far is Star Aqua's apoapsis if Star Aqua is considered 3.250 times faster in periapsis than in apoapsis. Note: You can ignore the gravitational interaction that exists between Star Aqua and Star Ruby. Use the figure to understand the problem better. Aqua periapsis Choices: a. 1.9x10¹¹ m b. 3.8x10¹1 m c. 3.6x10¹0 m d. 1.2x10¹¹ m Ruby Ai apoapsisarrow_forwardEarth is about 150 million kilometers from the Sun (1 Astronomical Unit, or AU), and the apparent brightness of the Sun in our sky is about 1300 watts/m^2. Using these two facts and the inverse square law for light, determine the apparent brightness that we would measure for the Sun if we were located at the following positions. a) At the orbit of Venus (67 million km from the Sun). b) At the orbit of Jupiter (780 million km from the Sun). c) At the mean distance of Pluto (40 Astronomical Units).arrow_forwardEarth is about 150 million kilometers from the Sun (1 Astronomical Unit, or AU), and the apparent brightness of the Sun in our sky is about 1300 watts/m^2. Using these two facts and the inverse square law for light, determine the apparent brightness that we would measure for the Sun if we were located at the following positions. b) At the orbit of Jupiter (780 million km from the Sun).arrow_forward
- The Algol binary system consists of a 3.7 Msun star and a 0.8 Msun star with an orbital period of 2.87 days. Using Newton’s version of Kepler’s Third Law, calculate the distance, a, between the two stars. Compare that to the size of Betelgeuse (you’ll need to look that up). Newton’s Version of Kepler’s Law: (M1 + M2) P2 = (4p2 /G) a3 Rearrange the equation to solve for a. Pi, p, is equal to 3.14. IMPORTANT NOTE: Google the value of G (the Universal Gravitational Constant) or look it up in your text. NOTICE THE UNITS. You must convert every distance and time in your equation to the same units, otherwise, you’ll get an incorrect answer. That means you must convert distances to meters, solar masses to kilograms, and time to seconds. When you compare your value to the size of Betelgeuse, it will also help that they are in the same units.arrow_forwardQuestion A1 Use a diagram to explain what is meant by the parallax angle, p, for a star observed twice from Earth, with a 6-month interval between each observation. Hence define the parsec, and calculate its value in astronomical units and metres. The star Betelgeuse is observed to have a parallax angle p = 4.5 x 10-³ arcseconds. State the distance of Betelgeuse in units of parsecs and light years.arrow_forwardSam is an astronomer on planet Hua, which orbits the distant star Barnard. It has recently been accepted that Hua is spherical in shape, although its exact size is unknown. While studying in the library, in the city of Joy, Sam learns that during equinox, Barnard is directly overhead in the city of Bar, located 1500.0 km north of his location. On the equinox, Sam goes outside and measures the altitude of Barnard at 83 degrees. What is the radius of Hua in km?arrow_forward
- A certain star has a parallax of 0.647 arcseconds. How far away is it (in metres)? [Type in the numerical value and units e.g. 1.23E+16m]arrow_forwardOn Earth, the parallax angle measured for the star Procyon is 0.29 arcseconds. If you were to measure Procyon's parallax angle from Venus, what would the parallax angle be? (Note: Earth's orbital radius is larger than Venus's orbital radius.) A. more than 0.29 arcseconds B. 0.29 arcseconds C. less than 0.29 arcseconds D.zero arcseconds (no parallax)arrow_forwardthe parallax angle of a star to be 0.002 arc-seconds. what would the distance be to this star?arrow_forward
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